1/(x+y) + 1/(x-y) = 7
4/(x+y) + 9/(x-y) = 53
Пусть 1/(x+y) = t, а 1/(x-y0 = u, тогда
t + u = 7
4t + 9u = 53
Умножим первое уравнение на -4
-4t - 4u = -28
Сложим оба уравнения
4t - 4t + 9u - 4u = 53 -28
5u = 25
Значит, u = 5
Так как t + 5 = 7, то t = 2
1/(x+y) = 2
1/(x-y) = 5
x + y = 1/2
x - y = 1/5
x = (1/2-y)
(1/2-y) - y = 1/5
1/2 - 2y = 1/5
2y = 1/2-1/5
2y = 3/10
y = 3/20
x = 1/2-3/20
x = 7/20
ответ: 7/20 и 3/20
1/(x+y) + 1/(x-y) = 7
4/(x+y) + 9/(x-y) = 53
Пусть 1/(x+y) = t, а 1/(x-y0 = u, тогда
t + u = 7
4t + 9u = 53
Умножим первое уравнение на -4
-4t - 4u = -28
4t + 9u = 53
Сложим оба уравнения
4t - 4t + 9u - 4u = 53 -28
5u = 25
Значит, u = 5
Так как t + 5 = 7, то t = 2
1/(x+y) = 2
1/(x-y) = 5
x + y = 1/2
x - y = 1/5
x = (1/2-y)
(1/2-y) - y = 1/5
x = (1/2-y)
1/2 - 2y = 1/5
x = (1/2-y)
2y = 1/2-1/5
x = (1/2-y)
2y = 3/10
x = (1/2-y)
y = 3/20
x = 1/2-3/20
y = 3/20
x = 7/20
y = 3/20
ответ: 7/20 и 3/20